Problem: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $n \neq 0$. $y = \dfrac{8n}{6(2n + 1)} \div \dfrac{7n}{6(2n + 1)} $
Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{8n}{6(2n + 1)} \times \dfrac{6(2n + 1)}{7n} $ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 8n \times 6(2n + 1) } { 6(2n + 1) \times 7n } $ $ y = \dfrac{48n(2n + 1)}{42n(2n + 1)} $ We can cancel the $2n + 1$ so long as $2n + 1 \neq 0$ Therefore $n \neq -\dfrac{1}{2}$ $y = \dfrac{48n \cancel{(2n + 1})}{42n \cancel{(2n + 1)}} = \dfrac{48n}{42n} = \dfrac{8}{7} $